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k-FRACTIONAL INTEGRAL INEQUALITIES FOR (h - m)-CONVEX FUNCTIONS VIA CAPUTO k-FRACTIONAL DERIVATIVES
Mishra, Lakshmi Narayan,Ain, Qurat Ul,Farid, Ghulam,Rehman, Atiq Ur The Kangwon-Kyungki Mathematical Society 2019 한국수학논문집 Vol.27 No.2
In this paper, first we obtain some inequalities of Hadamard type for (h - m)-convex functions via Caputo k-fractional derivatives. Secondly, two integral identities including the (n + 1) and (n+ 2) order derivatives of a given function via Caputo k-fractional derivatives have been established. Using these identities estimations of Hadamard type integral inequalities for the Caputo k-fractional derivatives have been proved.
UNIFIED INTEGRAL OPERATOR INEQUALITIES VIA CONVEX COMPOSITION OF TWO FUNCTIONS
Mishra, Lakshmi Narayan,Farid, Ghulam,Mahreen, Kahkashan The Kangwon-Kyungki Mathematical Society 2021 한국수학논문집 Vol.29 No.1
In this paper we have established inequalities for a unified integral operator by using convexity of composition of two functions. The obtained results are directly connected to bounds of various fractional and conformable integral operators which are already known in literature. A generalized Hadamard integral inequality is obtained which further leads to its various versions for associated fractional integrals. Further, some implicated results are discussed.
SOME COINCIDENCE AND COMMON FIXED POINT RESULTS IN MENGER SPACES
Lakshmi Narayan Mishra,Deepti Thakur,Rajinder Sharma 한국전산응용수학회 2021 Journal of Applied and Pure Mathematics Vol.3 No.1
In this paper, we established some common fixed point theorems for two pairs of self maps by using the notion of compatibility of type (E) along with weakly subsequential continuous (wsc) mappings in a Menger space. Common fixed point theorem satisfying an integral analogue is also given. Some examples in support of the proven results are also provided. Corresponding common fixed point theorem in metric spaces is also obtained as an application to our main result. We improve some earlier results in this line.
Solvability of some non-linear functional integral equations via measure of noncompactness
Deepak Dhiman,Lakshmi Narayan Mishra,Vishnu Narayan Mishra 장전수학회 2022 Advanced Studies in Contemporary Mathematics Vol.32 No.2
In this study, we establish some results related to the existence of solutions for nonlinear functional integral equations, by Darbo's fixed point theorem in Banach algebra, which contains several functional integral equations that arise in mathematical analysis. As an application, we also provide an example of functional integral equations.
DIPANKAR DAS,Lakshmi Narayan Mishra 장전수학회 2019 Advanced Studies in Contemporary Mathematics Vol.29 No.3
In this paper, we introduce C- algebra valued modular b- metric spaces. Some common xed point theorems for JHR operator pairs with new contractive conditions via C-class functions in C- algebra valued modular b-metric spaces is given here with examples. Some applications on non linear integral equation and on operator equation is also introduced.
Ramu Dubey,Lakshmi Narayan Mishra 장전수학회 2019 Advanced Studies in Contemporary Mathematics Vol.29 No.3
The motivation behind this paper is to study a class of nondierentiable multiobjective fractional program- ming problem in which each component of objective functions contains a term including the support function of a compact convex set. For a dierentiable function, we consider the class of second-order (F; ; ; d)-type- I convex functions. Further, we formulate unied (mixed type) dual models and derived duality relations under aforesaid assumptions.
FIXED POINT THEOREMS IN FUZZY METRIC SPACES FOR MAPPINGS WITH SOME CONTRACTIVE TYPE CONDITIONS
Patir, Bijoy,Goswami, Nilakshi,Mishra, Lakshmi Narayan The Kangwon-Kyungki Mathematical Society 2018 한국수학논문집 Vol.26 No.2
In this paper, we derive some fixed point theorems in fuzzy metric spaces for self mappings satisfying different contractive type conditions. Some of these theorems generalize some results of Wairojjana et al. (Fixed Point Theory and Applications (2015) 2015:69). Several examples in support of the theorems are also presented here.
ON THE POWER INTEGRABILITY WITH WEIGHT OF DOUBLE TRIGONOMETRIC SERIES
XHEVAT ZAHIR KRASNIQI,Lakshmi Narayan Mishra 장전수학회 2021 Advanced Studies in Contemporary Mathematics Vol.31 No.2
In this paper we have found the necessary and sufficient conditions for the power integrability with a weight of the sum of the double sine, double cosine series and double mixed sine-cosine series whose coefficients belong to a subclass of the γDRBV S class.
Supriya Kumar Paul,Lakshmi Narayan Mishra 강원경기수학회 2024 한국수학논문집 Vol.32 No.1
This paper consists of two significant aims. The first aim of this paper is to establish the criteria for the existence of solutions to nonlinear Volterra-Fredholm (V-F) fractional integral equations on $[0, L]$, where $0<L<\infty$. The fractional integral is described here in the sense of the Katugampola fractional integral of order $\lambda>0$ and with the parameter $\beta>0$. The concepts of the fixed point theorem and the measure of noncompactness are used as the main tools to prove the existence of solutions. The second aim of this paper is to introduce a computational method to obtain approximate numerical solutions to the considered problem. This method is based on the Fibonacci wavelets with collocation technique. Besides, the results of the error analysis and discussions of the accuracy of the solutions are also presented. To the best knowledge of the authors, this is the first computational method for this generalized problem to obtain approximate solutions. Finally, two examples are discussed with the computational tables and convergence graphs to interpret the efficiency and applicability of the presented method.
Gunaseelan Mani,A. Leema Maria Prakasam,Lakshmi Narayan Mishra,Vishnu Narayan Mishra 경남대학교 기초과학연구소 2021 Nonlinear Functional Analysis and Applications Vol.26 No.5
In this paper, we introduce the concepts of an orthogonal generalized F -contraction mapping and prove some fixed point theorems for a self mapping in an orthogonal metric space. The given results are generalization and extension some of the well-known results in the literature. An example to support our result is presented.