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Authors:Yogesh J. Bagul, Satish K. Panchal Pages: 01 - 07 Abstract: In this work, the authors present new lower and upper bounds for cos x and cosh x, thus improving some generalized inequalities of Kober and Lazarevic type. PubDate: 2022-01-27 DOI: 10.18311/jims/2022/20737 Issue No:Vol. 89, No. 1-2 (2022)

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Authors:Savita Bhatnagar Pages: 08 - 18 Abstract: We study the algebra of vector valued multipliers of Banach algebra valued McShane integrable functions. We prove that if X is a commutative Banach algebra, with identity e of norm one, then functions associated with measures of strong bounded variation and the set {L'([a, b],') e} are vector valued multipliers of McShane integrable functions. We find some necessary and another set of sufficient conditions for a functiong to define a multiplier. In case X satisfies Radon Nikodym property (weak Radon Nikodym property), we study multiplier operators. PubDate: 2022-01-27 DOI: 10.18311/jims/2022/29294 Issue No:Vol. 89, No. 1-2 (2022)

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Authors:Mohammad Reza Darafsheh, Reza Kahkeshani Pages: 19 - 31 Abstract: In this paper, we construct, using computations withMagma, a ternary code C from a primitive permutation representation of degree 15 of the group PSL2(9) by Key-Moori Method 1. The code C is an optimal code invariant under the group S6. We consider the action of the automorphism group S6 on C and its dual. By taking the support of any codeword ' of weight l and orbiting it under S6, 1-(15, l, kl) designs are obtained, where kl = l 'S6 /15. For any codeword, the structure of the stabilizer in S6 is determined and primitivity of S6 on each design is examined. It is shown that the complement of one of these designs is actually a new design D with parameters 2-(15, 7, 36). Moreover, Aut(D) ' S6. PubDate: 2022-01-27 DOI: 10.18311/jims/2022/23538 Issue No:Vol. 89, No. 1-2 (2022)

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Authors:Radha Madhavi Duggaraju, Lipika Mazumdar Pages: 32 - 43 Abstract: Let G = (V,E) be a graph of order n. Let R be a commutative ring and I denote the set of all ideals of R. Let ' : E ' I be an edge labeling. A generalized spline of (G, ') is a vertex labeling F : V ' R such that for each edge uv, F(u) ' F(v) ' '(uv). The set R(G,) of all generalized splines of (G, ') is an R-module. In this paper we determine conditions for a subset of R(G,') to form a basis of R(G,') for some classes of graphs. PubDate: 2022-01-27 DOI: 10.18311/jims/2022/29295 Issue No:Vol. 89, No. 1-2 (2022)

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Authors:Renukadevi S. Dyavanal, Madhura M. Mathai, Ashwini M. Hattikal Pages: 44 - 57 Abstract: In this work, we generalize the estimate of cardinality of a unique range set of meromorphic functions (URSM) and as an application we obtain the cardinality of URSM of a meromorphic function f(z) of finite order and its linear difference polynomial L(z, f). As a consequences we deduce several uniqueness of f(z) and L(z, f) sharing a set. PubDate: 2022-01-27 DOI: 10.18311/jims/2022/29306 Issue No:Vol. 89, No. 1-2 (2022)

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Authors:Prasenjit Ghosh, T. K. Samanta Pages: 58 - 71 Abstract: Generalized fusion frames and some of their properties in a tensor product of Hilbert spaces are studied. Also, the canonical dual g-fusion frame in a tensor product of Hilbert spaces is considered. The frame operator for a pair of g-fusion Bessel sequences in a tensor product of Hilbert spaces is presented. PubDate: 2022-01-27 DOI: 10.18311/jims/2022/29307 Issue No:Vol. 89, No. 1-2 (2022)

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Authors:Kunal Julal Ingale, Hemant Premraj Bendale, Dipak Ravindra Bonde, Jayprakash Ninu Chaudhari Pages: 72 - 83 Abstract: We introduce the concepts of a k-regular and a k-invertible additive ternary semiring. We show that (i) If I is a k-regular ideal of an additive ternary semiring S and J is any ideal of S, then I ' J is a k-regular ideal of S; (ii) If S is an additively idempotent, commutative additive ternary semiring and x ' S, then M (x) is a commutative additive ternary monoid of (S, +); (iii) An additively idempotent additive ternary semiring S is k-regular if and only if S is k-invertible; (iv) Let S be an additively and lateral cancellative additive ternary semiring. If a, b ' S, then V (a) and V (b) are either disjoint or equal. PubDate: 2022-01-27 DOI: 10.18311/jims/2022/29309 Issue No:Vol. 89, No. 1-2 (2022)

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Authors:Bruno De Malafosse Pages: 84 - 99 Abstract: Given any sequence a = (an)n'1 of positive real numbers and any set E of complex sequences, we write Ea for the set of all sequences y = (yn)n'1 such that y/a = (yn/an)n'1 ' E; in particular, ca, (or s(c) a ) denotes the set of all sequences y such that y/a converges. In this paper, we solve sequence spaces equations of the form (Ex)B(r,s) = Ea, where E 2 {c0, c, `1}. Then we apply these results to the solvability of each of the (SSE) with operators ca + cx = (cb)B(r,s) and ca + cx = (cb)G(,), where B (r, s) is a double band matrix, and G(, ) is the factorable matrix with positive sequences and , that is, the triangle whose the nonzero entries are defined by [G(, )]nk = nk. PubDate: 2022-01-27 DOI: 10.18311/jims/2022/29308 Issue No:Vol. 89, No. 1-2 (2022)

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Authors:Ankit Pal, R. K. Jana, A. K. Shukla Pages: 100 - 116 Abstract: In this paper, we address an extended version of pRq(' ' ') function using k-Pochhammer symbol and study their classical properties and generalized integral transform. Further, we study Pathway fractional hypergeometric integral and fractional derivatives of the extended pRq(' ' ') function. Some special cases have also been illustrated. PubDate: 2022-01-27 DOI: 10.18311/jims/2022/29310 Issue No:Vol. 89, No. 1-2 (2022)

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Authors:Ruchi Patel, Saurabh Porwal Pages: 117 - 133 Abstract: The main object of this paper is to obtain sharp lower bounds for the ratio of convolution of harmonic multivalent function to its sequences of partial sums. Relevant connections of the results presented here with various known results are briefly indicated. PubDate: 2022-01-27 DOI: 10.18311/jims/2022/24179 Issue No:Vol. 89, No. 1-2 (2022)

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Authors:Ashish Pathak, Prabhat Yadav, M. M. Dixit Pages: 134 - 144 Abstract: In this paper, we derive asymptotic expansion of the wavelet transform for small values of the dilation parameter a by using Lopez and Pagola technique. Asymptotic expansion of Morlet wavelet, Mexican Hat wavelet and Haar wavelet transform are obtained as a special cases. PubDate: 2022-01-27 DOI: 10.18311/jims/2022/29311 Issue No:Vol. 89, No. 1-2 (2022)

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Authors:S. G. Rayaguru, G. K. Panda Pages: 145 - 166 Abstract: In this paper, we derive the closed form expressions for the finite and infinite sums with summands having products of balancing and Lucas-balancing numbers in the denominator. We present some generalized Brousseau’s sums for balancing and Lucas-balancing numbers. PubDate: 2022-01-27 DOI: 10.18311/jims/2022/22177 Issue No:Vol. 89, No. 1-2 (2022)

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Authors:S. Sharma, M. Rana Pages: 167 - 171 Abstract: Combinatorial interpretations of the Rogers–Ramanujan identities are provided in terms of n–color partitions. Further interpretations in terms of ordinary partitions are obtained by using bijective maps. These results lead to the interpretations of two fifth order mock theta functions by attaching weights. PubDate: 2022-01-27 DOI: 10.18311/jims/2022/29312 Issue No:Vol. 89, No. 1-2 (2022)

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Authors:Smita Sonker, Rozy Jindal Pages: 172 - 181 Abstract: In this paper, we have proved a general theorem dealing with absolute Riesz Ñ, P','N;' ; ' K summablility by applying an almost increasing sequence. Also, some known results are also deduced. PubDate: 2022-01-27 DOI: 10.18311/jims/2022/29313 Issue No:Vol. 89, No. 1-2 (2022)

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Authors:Sarita Thakar, Pratiksha Demanna Pages: 182 - 197 Abstract: Multiplicity of eigenvalues of the regular indefinite Sturm- Liouville problem 'y"" + qy = 'wy on [a, b] subject to periodic boundary conditions is discussed. A necessary and sufficient condition for the existence of non-simple real eigenvalues is proved. Eigenfunctions corresponding to non-simple real eigenvalues are obtained. In this article, we discuss the interlacing property in one turning point case with periodic boundary conditions. PubDate: 2022-01-27 DOI: 10.18311/jims/2022/26181 Issue No:Vol. 89, No. 1-2 (2022)