Shehu Transform in Quantum Calculus and Its Applications

2022 ◽  
Vol 8 (1) ◽  
Author(s):  
Arvind Kumar Sinha ◽  
Srikumar Panda
Keyword(s):  
Quantum Calculus

New generalized 2D Ostrowski type inequalities on time scales with k2 points using a parameter

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3155-3169 ◽  
Author(s):  
Seth Kermausuor ◽  
Eze Nwaeze
Keyword(s):  
Numerical Analysis ◽  
Time Scales ◽  
Type Inequality ◽  
Dimensional Case ◽  
Multiple Points ◽  
Quantum Calculus ◽  
Independent Variables ◽  
Ostrowski Type Inequality ◽  
Two Independent Variables

Recently, a new Ostrowski type inequality on time scales for k points was proved in [G. Xu, Z. B. Fang: A Generalization of Ostrowski type inequality on time scales with k points. Journal of Mathematical Inequalities (2017), 11(1):41-48]. In this article, we extend this result to the 2-dimensional case. Besides extension, our results also generalize the three main results of Meng and Feng in the paper [Generalized Ostrowski type inequalities for multiple points on time scales involving functions of two independent variables. Journal of Inequalities and Applications (2012), 2012:74]. In addition, we apply some of our theorems to the continuous, discrete, and quantum calculus to obtain more interesting results in this direction. We hope that results obtained in this paper would find their place in approximation and numerical analysis.

scholarly journals Hermite–Hadamard Inclusions for Co-Ordinated Interval-Valued Functions via Post-Quantum Calculus

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1216
Author(s):  
Jessada Tariboon ◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Sotiris K. Ntouyas
Keyword(s):  
Variable Interval ◽  
Quantum Calculus ◽  
New Findings ◽  
Interval Valued

In this paper, the notions of post-quantum integrals for two-variable interval-valued functions are presented. The newly described integrals are then used to prove some new Hermite–Hadamard inclusions for co-ordinated convex interval-valued functions. Many of the findings in this paper are important extensions of previous findings in the literature. Finally, we present a few examples of our new findings. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role.

scholarly journals General Summation Formulas Contiguous to the q-Kummer Summation Theorems and Their Applications

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1102
Author(s):  
Yashoverdhan Vyas ◽  
Hari M. Srivastava ◽  
Shivani Pathak ◽  
Kalpana Fatawat
Keyword(s):  
Hypergeometric Functions ◽  
Theory Theory ◽  
Binomial Theorem ◽  
Generalized Hypergeometric Functions ◽  
Quantum Calculus ◽  
The Third ◽  
Summation Formulas ◽  
Symmetric Quantum ◽  
Summation Theorem

This paper provides three classes of q-summation formulas in the form of general contiguous extensions of the first q-Kummer summation theorem. Their derivations are presented by using three methods, which are along the lines of the three types of well-known proofs of the q-Kummer summation theorem with a key role of the q-binomial theorem. In addition to the q-binomial theorem, the first proof makes use of Thomae’s q-integral representation and the second proof needs Heine’s transformation. Whereas the third proof utilizes only the q-binomial theorem. Subsequently, the applications of these summation formulas in obtaining the general contiguous extensions of the second and the third q-Kummer summation theorems are also presented. Furthermore, the investigated results are specialized to give many of the known as well as presumably new q-summation theorems, which are contiguous to the three q-Kummer summation theorems. This work is motivated by the observation that the basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) gamma and q-hypergeometric functions and basic (or q-) hypergeometric polynomials, are applicable particularly in several diverse areas including Number Theory, Theory of Partitions and Combinatorial Analysis as well as in the study of Combinatorial Generating Functions. Just as it is known in the theory of the Gauss, Kummer (or confluent), Clausen and the generalized hypergeometric functions, the parameters in the corresponding basic or quantum (or q-) hypergeometric functions are symmetric in the sense that they remain invariant when the order of the p numerator parameters or when the order of the q denominator parameters is arbitrarily changed. A case has therefore been made for the symmetry possessed not only by hypergeometric functions and basic or quantum (or q-) hypergeometric functions, which are studied in this paper, but also by the symmetric quantum calculus itself.

scholarly journals Harmonic univalent functions defined by post quantum calculus operators

2019 ◽  
Vol 11 (1) ◽  
pp. 5-17 ◽  
Author(s):  
Om P. Ahuja ◽  
Asena Çetinkaya ◽  
V. Ravichandran
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disc ◽  
Quantum Calculus ◽  
Special Cases ◽  
The Family ◽  
Covering Theorems

Abstract We study a family of harmonic univalent functions in the open unit disc defined by using post quantum calculus operators. We first obtained a coefficient characterization of these functions. Using this, coefficients estimates, distortion and covering theorems were also obtained. The extreme points of the family and a radius result were also obtained. The results obtained include several known results as special cases.

scholarly journals INVESTIGATION OF SOME RESULTS ARISING FROM POST QUANTUM CALCULUS

2020 ◽  
Vol 20 (3) ◽  
pp. 561-572
Author(s):  
GHAZALA GULSHAN ◽  
RASHIDA HUSSAIN ◽  
ASGHAR ALI
Keyword(s):  
Quantum Calculus ◽  
Special Cases ◽  
Type Integral ◽  
Integral Identities

This article is pedestal for the (p,q)-calculus connecting two concepts of (p,q)-derivatives and (p,q)-integrals. The purpose of this paper is to establish different type of identities for (p,q)-calculus. Some special cases of the (p,q)-midpoint, Simpson, Averaged midpoint trapezoid, and trapezoid type integral identities are also derived.

scholarly journals Coefficient Estimates and the Fekete–Szegö Problem for New Classes of m-Fold Symmetric Bi-Univalent Functions

Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 129
Author(s):  
Georgia Irina Oros ◽  
Luminiţa-Ioana Cotîrlă
Keyword(s):  
Univalent Functions ◽  
Coefficient Estimates ◽  
Quantum Calculus

The results presented in this paper deal with the classical but still prevalent problem of introducing new classes of m-fold symmetric bi-univalent functions and studying properties related to coefficient estimates. Quantum calculus aspects are also considered in this study in order to enhance its novelty and to obtain more interesting results. We present three new classes of bi-univalent functions, generalizing certain previously studied classes. The relation between the known results and the new ones presented here is highlighted. Estimates on the Taylor–Maclaurin coefficients |am+1| and |a2m+1| are obtained and, furthermore, the much investigated aspect of Fekete–Szegő functional is also considered for each of the new classes.

The q-deformed mKP hierarchy with two parameters

2018 ◽  
Vol 32 (16) ◽  
pp. 1850170
Author(s):  
Kelei Tian ◽  
Yanyan Ge ◽  
Xiaoming Zhu
Keyword(s):  
Additional Symmetry ◽  
Lax Equation ◽  
Quantum Calculus ◽  
Two Parameters ◽  
Sato Theory

In this paper, with the help of the biparametric quantum calculus we construct the Sato theory on the q-deformation modified Kadomtsev–Petviashvili hierarchy with two parameters (qp-mKP), which is a new deformation of classical mKP hierarchy. The Lax equation and dressing operator of qp-mKP hierarchy are derived. By considering the M operator and [Formula: see text] operator, the additional symmetry of qp-mKP hierarchy is obtained.

Quantum calculus and quasiconformal mappings

2016 ◽  
Vol 100 (1-2) ◽  
pp. 123-131 ◽  
Author(s):  
A. G. Sergeev
Keyword(s):  
Quasiconformal Mappings ◽  
Quantum Calculus

scholarly journals A Dunkl type generalization of Szász operators via post-quantum calculus

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Abdullah Alotaibi ◽  
Md. Nasiruzzaman ◽  
M. Mursaleen
Keyword(s):  
Quantum Calculus ◽  
Szász Operators
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