International Journal of Analysis
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Open Access journal
ISSN (Print) 2314-498X - ISSN (Online) 2314-4998
Published by Hindawi [333 journals]
- Geraghty Type Generalized -Contractions and Related Applications in
Partial -Metric Spaces
Abstract: The purpose of this paper is to introduce new concepts of -admissible Geraghty type generalized -contraction and to prove that some fixed point results for such mappings are in the perspective of partial -metric space. As an application, we inaugurate new fixed point results for Geraghty type generalized graphic -contraction defined on partial metric space endowed with a directed graph. On the other hand, one more application to the existence and uniqueness of a solution for the first-order periodic boundary value problem is also provided. Our findings encompass various generalizations of the Banach contraction principle on metric space, partial metric space, and partial -metric space. Moreover, some examples are presented to illustrate the usability of the new theory.
PubDate: Wed, 15 Mar 2017 00:00:00 +000
- A Characterization of Bi-Jordan Homomorphisms on Banach Algebras
Abstract: For Banach algebras and , we show that if is unital and commutative, each bi-Jordan homomorphism from into a semisimple commutative Banach algebra is a bihomomorphism.
PubDate: Tue, 31 Jan 2017 00:00:00 +000
- Stability and Boundedness of Solutions to a Certain Second-Order
Nonautonomous Stochastic Differential Equation
Abstract: This paper focuses on stability and boundedness of certain nonlinear nonautonomous second-order stochastic differential equations. Lyapunov’s second method is employed by constructing a suitable complete Lyapunov function and is used to obtain criteria, on the nonlinear functions, that guarantee stability and boundedness of solutions. Our results are new; in fact, according to our observations from the relevant literature, this is the first attempt on stability and boundedness of solutions of second-order nonlinear nonautonomous stochastic differential equations. Finally, examples together with their numerical simulations are given to authenticate and affirm the correctness of the obtained results.
PubDate: Sun, 25 Dec 2016 08:59:37 +000
- Construction and Analysis of Binary Subdivision Schemes for Curves and
Surfaces Originated from Chaikin Points
Abstract: We present a new variant of Lane-Riesenfeld algorithm for curves and surfaces both. Our refining operator is the modification of Chaikin/Doo-Sabin subdivision operator, while each smoothing operator is the weighted average of the four/sixteen adjacent points. Our refining operator depends on two parameters (shape and smoothing parameters). So we get new families of univariate and bivariate approximating subdivision schemes with two parameters. The bivariate schemes are the nontensor product schemes for quadrilateral meshes. Moreover, we also present analysis of our families of schemes. Furthermore, our schemes give cubic polynomial reproduction for a specific value of the shape parameter. The nonuniform setting of our univariate and bivariate schemes gives better performance than that of the uniform schemes.
PubDate: Tue, 06 Dec 2016 14:28:17 +000
- Some New Ostrwoski’s Inequalities for Functions Whose th Derivatives
Abstract: We prove some new Ostrowski’s inequalities for functions whose th derivatives are -convex.
PubDate: Mon, 28 Nov 2016 13:41:13 +000
- Coefficient Estimates for Certain Subclasses of Biunivalent Functions
Defined by Convolution
Abstract: We introduce two new subclasses of the function class of biunivalent functions in the open disc defined by convolution. Estimates on the coefficients and for the two subclasses are obtained. Moreover, we verify Brannan and Clunie’s conjecture for our subclasses.
PubDate: Tue, 22 Nov 2016 14:36:34 +000
- Multiplicity of Solutions for Schrödinger Equations with
Abstract: We study the multiplicity of solutions for a class of semilinear Schrödinger equations: where satisfies some kind of coercive condition and involves concave-convex nonlinearities with indefinite signs. Our theorems contain some new nonlinearities.
PubDate: Tue, 22 Nov 2016 09:39:02 +000
- A Generalization on Weighted Means and Convex Functions with respect to
the Non-Newtonian Calculus
Abstract: This paper is devoted to investigating some characteristic features of weighted means and convex functions in terms of the non-Newtonian calculus which is a self-contained system independent of any other system of calculus. It is shown that there are infinitely many such useful types of weighted means and convex functions depending on the choice of generating functions. Moreover, some relations between classical weighted mean and its non-Newtonian version are compared and discussed in a table. Also, some geometric interpretations of convex functions are presented with respect to the non-Newtonian slope. Finally, using multiplicative continuous convex functions we give an application.
PubDate: Tue, 22 Nov 2016 09:32:28 +000
- Strong -Convexity and Separation Theorems
Abstract: Jensen inequality for strongly -convex functions and a characterization of pairs of functions that can be separated by a strongly -convex function are presented. As a consequence, a stability result of the Hyers-Ulam type is obtained.
PubDate: Thu, 10 Nov 2016 11:15:46 +000
- Straightforward Proofs of Ostrowski Inequality and Some Related Results
Abstract: We give proofs of some known results in very simple and antique way. Also we find some general bounds of a nonnegative difference of the Hadamard inequality and an Ostrowski-Grüss type inequality is proved.
PubDate: Wed, 09 Nov 2016 09:39:22 +000
- On the Marginal Distribution of the Diagonal Blocks in a Blocked Wishart
Abstract: Let be a blocked Wishart random matrix with diagonal blocks of orders and . The goal of the paper is to find the exact marginal distribution of the two diagonal blocks of . We find an expression for this marginal density involving the matrix-variate generalized hypergeometric function. We became interested in this problem because of an application in spatial interpolation of random fields of positive definite matrices, where this result will be used for parameter estimation, using composite likelihood methods.
PubDate: Tue, 01 Nov 2016 06:27:22 +000
- Inclusion of the Generalized Bessel Functions in the Janowski Class
Abstract: Sufficient conditions on , , , , and are determined that will ensure the generalized Bessel function satisfies the subordination . In particular this gives conditions for , , to be close-to-convex. Also, conditions for to be Janowski convex and to be Janowski starlike in the unit disk are obtained.
PubDate: Thu, 27 Oct 2016 12:27:22 +000
- Hermite-Hadamard Type Inequalities Obtained via Fractional Integral for
Differentiable -Convex and -Convex Functions
Abstract: Some Hermite-Hadamard type inequalities involving fractional integrals for -convex and ()-convex functions are obtained.
PubDate: Thu, 20 Oct 2016 06:51:24 +000
- Common Fixed Point Results for Six Mappings via Integral Contractions with
Abstract: Common fixed point theorems for six self-mappings under integral type inequality satisfying and properties in the context of complex valued metric space (not necessarily complete) are established. The derived results are new even for ordinary metric spaces. We prove existence result for optimal unique solution of the system of functional equations used in dynamical programming with complex domain.
PubDate: Wed, 19 Oct 2016 07:14:20 +000
- Some Nonlinear Stochastic Cauchy Problems with Generalized Stochastic
Abstract: We study some nonlinear stochastic Cauchy problems in the framework of the -algebras. We adapt the definitions to this framework. By means of suitable regularizations, we define associated generalized problems. We use our previous results about the wave equation in canonical form to obtain generalized solutions. We compare the generalized solutions with the classical ones when they exist.
PubDate: Tue, 18 Oct 2016 13:38:27 +000
- Hyers-Ulam Stability of Fractional Nabla Difference Equations
Abstract: We investigate the Hyers-Ulam stability, the generalized Hyers-Ulam stability, and the -Hyers-Ulam stability of a linear fractional nabla difference equation using discrete Laplace transform. We provide a few examples to illustrate the applicability of established results.
PubDate: Wed, 21 Sep 2016 11:42:44 +000
- On Faster Implicit Hybrid Kirk-Multistep Schemes for Contractive-Type
Abstract: The purpose of this paper is to prove strong convergence and T-stability results of some modified hybrid Kirk-Multistep iterations for contractive-type operator in normed linear spaces. Our results show through analytical and numerical approach that the modified hybrid schemes are better in terms of convergence rate than other hybrid Kirk-Multistep iterative schemes in the literature.
PubDate: Mon, 19 Sep 2016 14:22:04 +000
- Variational-Like Inequalities for Weakly Relaxed Pseudomonotone Set-Valued
Mappings in Banach Space
Abstract: We introduce and study variational-like inequalities for generalized pseudomonotone set-valued mappings in Banach spaces. By using KKM technique, we obtain the existence of solutions for variational-like inequalities for generalized pseudomonotone set-valued mappings in reflexive Banach spaces. The results presented in this paper are generalizations and improvements of the several well-known results in the literature.
PubDate: Wed, 07 Sep 2016 16:45:04 +000
- Retracted: Quasilinear Inner Product Spaces and Hilbert Quasilinear Spaces
PubDate: Sun, 21 Aug 2016 06:32:42 +000
- Some Congruence Properties of a Restricted Bipartition Function
Abstract: Let denote the number of bipartitions of a positive integer subject to the restriction that each part of is divisible by . In this paper, we prove some congruence properties of the function for , 11, and , for any integer , by employing Ramanujan’s theta-function identities.
PubDate: Mon, 08 Aug 2016 07:54:11 +000
- On Inclusion Relations between Some Sequence Spaces
Abstract: We determine the relations between the classes of almost -statistically convergent sequences and the relations between the classes of strongly almost -summable sequences for various sequences , in the class . Furthermore we also give the relations between the classes of almost -statistically convergent sequences and the classes of strongly almost -summable sequences for various sequences .
PubDate: Wed, 03 Aug 2016 08:06:15 +000
- Fixed Point Theorems for Geraghty Type Contractive Mappings and Coupled
Fixed Point Results in 0-Complete Ordered Partial Metric Spaces
Abstract: We establish new fixed point theorems in 0-complete ordered partial metric spaces. Also, we give remark on coupled generalized Banach contraction. Some examples illustrate the usability of our results. The theorems presented in this paper are generalizations and improvements of the several well known results in the literature.
PubDate: Wed, 03 Aug 2016 07:47:41 +000
- On a Fixed Point Theorem with Application to Integral Equations
Abstract: We introduce the notion of dualistic Geraghty’s type contractions. We prove some fixed point theorems for ordered mappings satisfying the abovementioned contractions. We discuss an application of our fixed point results to show the existence of solution of integral equations.
PubDate: Mon, 30 May 2016 08:48:12 +000
- Singular Differential Equations and -Drazin Invertible Operators
Abstract: We extend results of Favini, Nashed, and Zhao on singular differential equations using the -Drazin inverse and the order of a quasinilpotent operator in the sense of Miekka and Nevanlinna. Two classes of singularly perturbed differential equations are studied using the continuity properties of the -Drazin inverse obtained by Koliha and Rakočević.
PubDate: Tue, 15 Mar 2016 11:38:07 +000
- Cyclicity of Special Operators on a BK with AK Space
Abstract: Let be a complex domain and let be a reflexive BK space with AK such that and the functional of evaluation at is bounded for all . We will investigate the cyclicity for the adjoint of a weighted composition operator acting on .
PubDate: Mon, 21 Dec 2015 11:59:14 +000
- A Survey on Operator Monotonicity, Operator Convexity, and Operator Means
Abstract: This paper is an expository devoted to an important class of real-valued functions introduced by Löwner, namely, operator monotone functions. This concept is closely related to operator convex/concave functions. Various characterizations for such functions are given from the viewpoint of differential analysis in terms of matrix of divided differences. From the viewpoint of operator inequalities, various characterizations and the relationship between operator monotonicity and operator convexity are given by Hansen and Pedersen. In the viewpoint of measure theory, operator monotone functions on the nonnegative reals admit meaningful integral representations with respect to Borel measures on the unit interval. Furthermore, Kubo-Ando theory asserts the correspondence between operator monotone functions and operator means.
PubDate: Wed, 11 Nov 2015 09:13:36 +000
- Some Ostrowski Type Inequalities for Harmonically -Convex Functions in
Abstract: The authors introduce the concept of harmonically -convex functions in second sense and establish some Ostrowski type inequalities of these classes of functions.
PubDate: Mon, 26 Oct 2015 12:34:27 +000
- On Equalities Involving Integrals of the Logarithm of the Riemann
-Function with Exponential Weight Which Are Equivalent to the Riemann
Abstract: Integral equalities involving integrals of the logarithm of the Riemann -function with exponential weight functions are introduced, and it is shown that an infinite number of them are equivalent to the Riemann hypothesis. Some of these equalities are tested numerically. The possible contribution of the Riemann function zeroes nonlying on the critical line is rigorously estimated and shown to be extremely small, in particular, smaller than nine milliards of decimals for the maximal possible weight function exp(). We also show how certain Fourier transforms of the logarithm of the Riemann zeta-function taken along the real (demi)axis are expressible via elementary functions plus logarithm of the gamma-function and definite integrals thereof, as well as certain sums over trivial and nontrivial Riemann function zeroes.
PubDate: Sun, 18 Oct 2015 16:22:19 +000
- On Simultaneous Approximation of Modified Baskakov-Durrmeyer Operators
Abstract: We discuss properties of modified Baskakov-Durrmeyer-Stancu (BDS) operators with parameter . We compute the moments of these modified operators. Also, we establish pointwise convergence, Voronovskaja type asymptotic formula, and an error estimation in terms of second order modification of continuity of the function for the operators .
PubDate: Sun, 18 Oct 2015 13:04:37 +000
- Geometric Properties of a Class of Analytic Functions Defined by a
Abstract: Let be the class of analytic functions defined in the open unit disk and normalized by . For in , let , where and . In the present paper, we find conditions under which functions in the class are starlike of order , .
PubDate: Sun, 04 Oct 2015 17:06:01 +000