Madan Mohan Soren

In this paper, we introduce the multiplicative generalized 𝑘-fractional conformable (MK-FCI) left and right integrals and investigate their fundamental properties, including integrability, boundedness, continuity, and the semigroup property. We then establish Hermite–Hadamard (HH) inequalities for these integrals, and further derive midpoint and trapezoidal inequalities as consequences of the obtained Hermite–Hadamard results. We also show how these new inequalities generalize and connect to existing results for multiplicative generalized 𝑘-fractional conformable integrals and classical multiplicative integrals through particular cases. Furthermore, we present novel Hermite–Hadamard, midpoint, and trapezoidal-type inequalities specifically tailored to the MK-FCI framework.

In the present study, we establish both pointwise and uniform convergence in the space of logarithmically uniformly continuous and bounded functions for the max-product and max-min Durrmeyer-type exponential sampling operators. Furthermore, the modular convergence of these operators is demonstrated within the framework of Orlicz space. In addition to the theoretical results, we provide numerical and graphical analyses for various kernel pairs, illustrating the convergence rates and approximation behavior of the proposed operators.

This article discusses the convergence properties of the Max Product and Max Min variants of Durrmeyer type exponential sampling series. We first establish pointwise and uniform convergence of both operators in the space of log uniformly continuous and bounded functions. The rates of convergence are then analyzed in terms of the logarithmic modulus of continuity. Additionally, the approximation errors of the proposed operators are examined using a variety of kernel functions. Finally, graphical illustrations are provided to demonstrate the convergence behavior of both operators.

In this current work, we propose a Max Min approach for approximating functions using exponential neural network operators. We extend this framework to develop the Max Min Kantorovich-type exponential neural network operators and investigate their approximation properties. We study both pointwise and uniform convergence for univariate functions. To analyze the order of convergence, we use the logarithmic modulus of continuity and estimate the corresponding rate of convergence. Furthermore, we examine the convergence behavior of the Max Min Kantorovich type exponential neural network operators within the Orlicz space setting. We provide some graphical representations to illustrate the approximation error of the function through suitable kernel and sigmoidal activation functions.

This study focuses on differential subordination using arithmetic and geometric approaches when the dominant function is linear. In addition to the results of differential subordination of arithmetic and geometric means in which a convex function was dominant, one can study such differential subordination for a selected convex function. We investigate several results of the differential subordinations of analytic functions are associated with an operator built using arithmetic and geometric means.