Band 45, Heft 1

We study Chern flat, Chern–Ricci flat twisted product almost Hermitian manifolds. We extend the twisted product to almost Hermitian manifolds, and give some formulae of the Chern curvature, the Chern–Ricci curvature and the Chern scalar curvature on the twisted product almost Hermitian manifold under the quasi-Kähler condition.

In this paper, we give the matrix version of Horn’s hypergeometric function and their confluent cases. We also discuss the regions of convergence, system of matrix differential equations of bilateral type, differential formulae and infinite summation formulae satisfied by these hypergeometric matrix functions. With the study of these 23 matrix functions, matrix generalization of Horn’s list of 34 hypergeometric series will be completed.

The modular fuzzy b -metric space is defined in this study, and we are interested in proving a general common fixed point theorem for a pair of multi-valued mappings in Hausdorff modular fuzzy b -metric spaces. The work generalizes the findings in [H. Kerim, W. Shatanawi, A. Tallafha and T. A. M. Shatnawi, Fixed point theorems on modular fuzzy metric spaces, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 84 2022, 1, 47–58] and produce additional specific findings that are supported by examples. An application to prove the existence of an integral inclusion equation’s solution is shown to demonstrate the importance of our result.

In this paper we find conditions for the boundedness of the strong and weak fractional integral and fractional maximal operator generated by Gegenbauer differential operator on G -Morrey spaces.

We introduce new extension of the extended Pochhammer symbol and gamma function by using the extended Mittag-Leffler function. We also present extension of the generalized hypergeometric function as well as some of their special cases by using this extended Pochhammer symbol. Further, we define the extension of the τ-Gauss hypergeometric function. Integral and derivative formulas involving the Mellin transform and fractional calculus techniques associated with this extended τ-Gauss hypergeometric function are also given. Also, new extended τ-Gauss hypergeometric function also provides a few more interesting and well-known results. This enriches the theory of special functions. The obtained results are believed to be newly presented.

In this article, we aim to present a new extension of the beta-logarithmic function with the help of an extended beta function and logarithmic mean. Then we introduce its statistical properties and investigate some basic important formulas of extended beta-logarithmic functions, such as integral representation, summation formula and Mellin transform. Further, we consider a new type of hypergeometric and confluent hypergeometric functions using this extended beta-logarithmic function and discuss their various result.

Let ν be a Borel probability measure on ℝ d {\mathbb{R}^{d}} and q , t ∈ ℝ {q,t\in\mathbb{R}} . This study takes a broad approach to the multifractal and fractal analysis problem and proposes an intrinsic definition of the general Hausdorff and packing measures by taking into account sums of the type ∑ i h - 1 ⁢ ( q ⁢ h ⁢ ( ν ⁢ ( B ⁢ ( x i , r i ) ) ) + t ⁢ g ⁢ ( r i ) ) \sum_{i}h^{-1}(qh(\nu(B(x_{i},r_{i})))+tg(r_{i})) for some prescribed functions h and g . The aim of this paper is to study the descriptive set-theoretic complexity and measurability of these measures and related dimension maps.