Saleem Ullah

Bio: Saleem Ullah is an academic researcher from Air University (Islamabad). The author has contributed to research in topics: Convex function & Convexity. The author has an hindex of 7, co-authored 14 publications receiving 113 citations. Previous affiliations of Saleem Ullah include COMSATS Institute of Information Technology.

Inequalities for a Unified Integral Operator and Associated Results in Fractional Calculus

Abstract: Integral operators are useful in real analysis, mathematical analysis, functional analysis and other subjects of mathematical approach. The goal of this paper is to study a unified integral operator via convexity. By using convexity and conditions of unified integral operators, bounds of these operators are obtained. Furthermore consequences of these results are discussed for fractional and conformable integral operators.

Generalized fractional inequalities for quasi-convex functions

Abstract: The class of quasi-convex functions contain all those finite convex functions which are defined on finite closed intervals of real line. The aim of this paper is to establish the bounds of the sum of left and right fractional integral operators using quasi-convex functions. An identity is formulated which is used to find Hadamard-type inequalities for quasi-convex functions. Connections with some known results are analyzed. Furthermore, some implications are derived by considering some examples of quasi-convex functions.

Spatial distribution of heavy metal and risk indices of water and sediments in the Kunhar River and its tributaries

Abstract: The present study investigated heavy metal (HM) concentrations in water and sediment of the Kunhar River and its tributaries in Kaghan valley, Northern Pakistan. The highest mean concentration was ...

Physical aspects of the Jeffery fluid inducing homogeneous–heterogeneous reactions in MHD flow: a Cattaneo–Christov approach

Abstract: This work is to elaborate the Jeffery stagnation point flow towards a cylindrical surface with the homogenous–heterogeneous reactions, magnetic field, and heat generation effects. The heat transpor...

Opial-type inequalities for convex functions and associated results in fractional calculus

Abstract: This paper is dedicated to Opial-type inequalities for arbitrary kernels using convex functions. These inequalities are further applied to a power function. Applications of the presented results are studied in fractional calculus via fractional integral operators by associating special kernels.

Operators of Basic (or q-) Calculus and Fractional q-Calculus and Their Applications in Geometric Function Theory of Complex Analysis

Abstract: Basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and basic (or q-) hypergeometric polynomials, are known to have widespread applications, particularly in several areas of number theory and combinatorial analysis such as (for example) the theory of partitions. Our usages here, in this survey-cum-expository article, of the q-calculus and the fractional q-calculus in geometric function theory of complex analysis are believed to encourage and motivate significant further developments on these and other related topics. By applying a fractional q-calculus operator, we define the subclasses $${\mathcal{S}}_{n}^{\alpha }(\lambda ,\beta ,b,q)$$ and $${\mathcal{G}}_{n}^{\alpha }(\lambda ,\beta ,b,q)$$ of normalized analytic functions with complex order and negative coefficients. Among the results investigated for each of these function classes, we derive their associated coefficient estimates, radii of close-to-convexity, starlikeness and convexity, extreme points and growth and distortion theorems. Our investigation here is motivated essentially by the fact that basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and basic (or q-) hypergeometric polynomials, are applicable particularly in several areas of number theory such as the theory of partitions. In fact, basic (or q-) hypergeometric functions are useful also in a wide variety of fields including, for example, combinatorial analysis, finite vector spaces, lie theory, particle physics, nonlinear electric circuit theory, mechanical engineering, theory of heat conduction, quantum mechanics, cosmology and statistics (see also (Srivastava and Karlsson in Multiple Gaussian hypergeometric series. pp 350–351, 1985) and the references cited thereon). In the last section on conclusion, we choose to point out the fact that the results for the q-analogues, which we consider in this article for $$0< q < 1$$, can easily (and possibly trivially) be translated into the corresponding results for the (p, q)-analogues (with $$0< q < p \leqq 1$$) by applying some obvious parametric and argument variations, the additional parameter p being redundant. Several other families of such extensively- and widely-investigated linear convolution operators as (for example) the Dziok–Srivastava, Srivastava–Wright and Srivastava–Attiya linear convolution operators, together with their extended and generalized versions, are also briefly considered.

Self-adaptive projection methods for the multiple-sets split feasibility problem

Abstract: The multiple-sets split feasibility problem (MSFP) is to find a point closest to the intersection of a family of closed convex sets in one space, such that its image under a linear transformation will be closest to the intersection of another family of closed convex sets in the image space. This problem arises in many practical fields, and it can be a model for many inverse problems. Noting that some existing algorithms require estimating the Lipschitz constant or calculating the largest eigenvalue of the matrix, in this paper, we first introduce a self-adaptive projection method by adopting Armijo-like searches to solve the MSFP, then we focus on a special case of the MSFP and propose a relaxed self-adaptive method by using projections onto half-spaces instead of those onto the original convex sets, which is much more practical. Convergence results for both methods are analyzed. Preliminary numerical results show that our methods are practical and promising for solving larger scale MSFPs.

Fractional generalized Hadamard and Fejér-Hadamard inequalities for m -convex functions

Abstract: The objective of this paper is to present the fractional Hadamard and Fejer-Hadamard inequalities in generalized forms. By employing a generalized fractional integral operator containing extended generalized Mittag-Leffler function involving a monotone increasing function, we generalize the well known fractional Hadamard and Fejer-Hadamard inequalities for m-convex functions. Also we study the error bounds of these generalized inequalities. In connection with some published results from presented inequalities are obtained.

Projection iterative methods for extended general variational inequalities

Abstract: In this paper, we introduce and study a new class of variational inequalities involving three operators, which is called the extended general variational inequality. Using the projection technique, we show that the extended general variational inequalities are equivalent to the fixed point and the extended general Wiener-Hopf equations. This equivalent formulation is used to suggest and analyze a number of projection iterative methods for solving the extended general variational inequalities. We also consider the convergence of these new methods under some suitable conditions. Since the extended general variational inequalities include general variational inequalities and related optimization problems as special cases, results proved in this paper continue to hold for these problems.