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GENERALIZATION OF THE FEJÉR-HADAMARD'S INEQUALITY FOR CONVEX FUNCTION ON COORDINATES
Farid, Ghulam,Rehman, Atiq Ur Korean Mathematical Society 2016 대한수학회논문집 Vol.31 No.1
In this paper, we give generalization of the $Fej\acute{e}r$-Hadamard inequality by using definition of convex functions on n-coordinates. Results given in [8, 12] are particular cases of results given here.
GHULAM FARID,LAXMI RATHOUR,SIDRA BIBI,MUHAMMAD SAEED AKRAM,LAKSHMI NARAYAN MISHRA,VISHNU NARAYAN MISHRA The Korean Society for Computational and Applied M 2023 Journal of applied and pure mathematics Vol.5 No.1/2
The Hadamard type inequalities for fractional integral operators of convex functions are studied at very large scale. This paper provides the Hadamard type inequalities for refined (α,h-m)-convex functions by utilizing Liouville-Caputo fractional (L-CF) derivatives. These inequalities give refinements of already existing (L-CF) inequalities of Hadamard type for many well known classes of functions provided the function h is bounded above by ${\frac{1}{\sqrt{2}}}$.
Ghulam Farid,Laxmi Rathour,Muhammad Saeed Akram,Sidra Bibi,Lakshmi Narayan Mishra,Vishnu Narayan Mishra 한국전산응용수학회 2023 Journal of Applied and Pure Mathematics Vol.5 No.1
The Hadamard type inequalities for fractional integral operators of convex functions are studied at very large scale. This paper provides the Hadamard type inequalities for refined ($\alpha$,$h$-$m$)-convex functions by utilizing Liouville-Caputo fractional (L-CF) derivatives. These inequalities give refinements of already existing (L-CF) inequalities of Hadamard type for many well known classes of functions provided the function $h$ is bounded above by $\frac{1}{\sqrt{2}}$.
On Opial-type inequalities via a new generalized integral operator
Ghulam Farid,Yasir Mehboob 강원경기수학회 2021 한국수학논문집 Vol.29 No.2
Opial inequality and its consequences are useful in establishing existence and uniqueness of solutions of initial and boundary value problems for differential and difference equations. In this paper we analyze Opial-type inequalities for convex functions. We have studied different versions of these inequalities for a generalized integral operator. Further difference of Opial-type inequalities are utilized to obtain generalized mean value theorems, which further produce various interesting derivations for fractional and conformable integral operators.
Ghulam Farid,Saira Bano Akbar,Laxmi Rathour,Lakshmi Narayan Mishra 강원경기수학회 2021 한국수학논문집 Vol.29 No.4
The refinement of an inequality provides better convergence of one quantity towards the other one. We have established the refinements of Hadamard inequalities for Riemann-Liouville fractional integrals via strongly $({\alpha},m)$-convex functions. In particular, we obtain two refinements of the classical Hadamard inequality. By using some known integral identities we also give refinements of error bounds of some fractional Hadamard inequalities.
Ghulam Farid,Sidra Bibi,Laxmi Rathour,Lakshmi Narayan Mishra,Vishnu Narayan Mishra 강원경기수학회 2023 한국수학논문집 Vol.31 No.1
We aim in this article to establish variants of the Hadamard inequality for Caputo fractional derivatives. We present the Hadamard inequality for strongly $(s,m)$-convex functions which will provide refinements as well as generalizations of several such inequalities already exist in the literature. The error bounds of these inequalities are also given by applying some known identities. Moreover, various associated results are deduced.
EXTENDED GENERALIZED MITTAG-LEFFLER FUNCTION APPLIED ON FRACTIONAL INTEGRAL INEQUALITIES
Andric, Maja,Farid, Ghulam,Pecaric, Josip,Siddique, Muhammad Usama Korean Mathematical Society 2020 대한수학회논문집 Vol.35 No.4
This paper presents several fractional generalizations and extensions of known integral inequalities. To obtain these, an extended generalized Mittag-Leffler function and its fractional integral operator are used.
A Systematic Review on the Mental Health Status of Patients Infected With Monkeypox Virus
Jaleel Anila,Farid Ghulam,Irfan Haleema,Mahmood Khalid,Baig Saeeda 대한소아청소년 정신의학회 2024 소아청소년정신의학 Vol.35 No.2
Objectives: This study aims to extract and summarize the literature on the mental health status of patients with monkeypox. Methods: This review was carried out according to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines using different databases and publishers such as Scopus, Sage, ScienceDirect, PubMed, BMJ, Wiley Online Library, Wolters Kluwer OVID-SP, and Google Scholar. The literature review was based on monkeypox and mental health. The year of publication was 2021–2023, during the monkeypox disease period. Data were extracted from opinions, editorials, empirical studies, and surveys. Results: Based on the literature related to the mental status of patients with monkeypox, the following themes and subthemes were identified: anxiety and depression, self-harm and suicidal tendencies, neuropsychiatric symptoms, mental health, social stigma, sex workers, vaccination, and stress-related diseases. Conclusion: A review of monkeypox virus infection studies reveals that 25%–50% of patients experience anxiety and depression due to isolation, boredom, and loneliness. Factors such as infected people, a lack of competence among healthcare professionals, and shame over physical symptoms exacerbate mental insults. The implications of society include increased self-harm, suicide, low productivity, fear of stigmatization, and transmission of infection.
Extended generalized Mittag-Leffler function applied on fractional integral inequalities
Maja Andric,Ghulam Farid,Josip Pecaric,Muhammad Usama Siddique 대한수학회 2020 대한수학회논문집 Vol.35 No.4
This paper presents several fractional generalizations and extensions of known integral inequalities. To obtain these, an extended generalized Mittag-Leffler function and its fractional integral operator are used.
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.