In this paper, we give a generalized definition namely strongly - convex function that unifies many known definitions. By applying this new definition, we present inequalities for unified integral operators which have connection with many of the well-known results for different kinds of convex functions. Moreover, this paper at once provides refinements and generalizations of a lot of fractional integral inequalities which are identified in remarks.

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Inequalities for Unified Integral Operators via Strongly α , h ‐ m -Convexity

This paper aims to obtain the bounds of a class of integral operators containing Mittag–Leffler functions in their kernels. A recently defined unified Mittag–Leffler function plays a vital role in connecting the results of this paper with the well-known bounds of fractional integral operators published in the recent past. The symmetry of a function about a line is a fascinating property that plays an important role in mathematical inequalities. A variant of the Hermite–Hadamard inequality is established using the closely symmetric property for (α,m)-convex functions.

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Generalization of Some Fractional Integral Operator Inequalities for Convex Functions via Unified Mittag-Leffler Function

In this paper, we study integral inequalities which will provide refinements of bounds of unified integral operators established for convex and - convex functions. A new definition of function, namely, strongly - convex function is applied in different forms and an extended Mittag-Leffler function is utilized to get the required results. Moreover, the obtained results in special cases give refinements of fractional integral inequalities published in this decade.

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Inequalities for a Unified Integral Operator for Strongly α , m -Convex Function and Related Results in Fractional Calculus

In this paper, we define a strongly exponentially - convex function that generates several kinds of strongly convex and convex functions. The left and right unified integral operators of these functions satisfy some integral inequalities which are directly related to many unified and fractional integral inequalities. From the results of this paper, one can obtain various fractional integral operator inequalities that already exist in the literature.

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On Generalized Strongly Convex Functions and Unified Integral Operators

Given n vertices and m edges, m ≥ 1, and for every vertex is given a label, there are lots of graphs that can be obtained. The graphs obtained may be simple or not simple, connected or disconnected. A graph G(V,E) is called simple if G(V,E) not containing loops nor paralel edges. An edge which has the same end vertex is called a loop, and paralel edges are two or more edges which connect the same set of vertices. Let N(G7,m,t) as the number of connected vertex labeled graphs of order seven with m vertices and t (t is the number edges that connect different pair of vertices). The result shows that N(G7,m,t) = ct C (m−1) t−1, with c6=6727, c7=30160 , c8=30765, c9=21000, c10=28364, c11=26880, c12=26460, c13=20790, c14=10290, c15= 8022, c16=2940, c17=4417, c18=2835, c19=210, c20= 21, c21=1.

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Determining The Number of Connected Vertex Labeled Graphs of Order Seven without Loops by Observing The Patterns of Formula for Lower Order Graphs with Similar Property

In today’s technological world, confidentiality is an important issue to deal with, and it is carried out through different proficiencies. Cryptography is a scientific technique of securing a communication from unauthenticated approach. There exist many encryption algorithms in cryptography for data security. The need of new nonstandard encryption algorithms has been raised to prevent the communication from traditional attacks. This paper proposes some new encryption algorithms for secure transmission of messages using some special corona graphs and bipartite graph along with some algebraic properties. These proposed encryption schemes will lead to more secure communication of secret messages.

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Some Graph-Based Encryption Schemes

Recently, a unified integral operator has been introduced by Farid, 2020, which produces several kinds of known fractional and conformable integral operators defined in recent decades (Kwun, 2019, Remarks 6 and 7) The aim of this paper is to establish bounds of this unified integral operator by means of - convex functions The resulting inequalities provide the bounds of all associated fractional and conformable integral operators in a compact form Also, the results of this paper hold for different kinds of convex functions connected with - convex functions

/pdf/inequalities-for-a-unified-integral-operator-via-a-m-convex-1na1reyapc.pdf

Baizhu Ni

Papers

Some Graph-Based Encryption Schemes

Inequalities for a Unified Integral Operator via α,m-Convex Functions