In this article, we define and investigate the concept of generalized 𝛾-preinvex function on the Yang's fractal set R 𝜉 (0 < 𝜉 ≤ 1). Based on the auxiliary definitions and involving local fractional integrals, we established several generalizations of Hermite-Hadamard type inequalities under certain conditions. Additionally, we discuss some examples to test our outcomes and some applications in the form of bounds for generalized r th moment of a continuous random variable.
The main objective of this paper is to study a new family of analytic functions that are q-starlike with respect to m-symmetrical points and subordinate to the q-Janowski function. We investigate inclusion results, sufficient conditions, coefficients estimates, bounds for Fekete–Szego functional |a3−μa22| and convolution properties for the functions belonging to this new class. Several consequences of main results are also obtained.
I dedicate this dissertation to my beloved sons, Hashem and Bassel, both of whom, I love so very dearly, and I miss them tremendously. I am proud to be their father, they have taught me the true meaning of life, and gave me love, happiness, and hope. Also I dedicate this work and give special thanks to my beloved and wonderful mother. Her support, encouragement, and constant love have sustained me throughout my life. Without you this would not have been possible. Finally, I would like to dedicate this thesis to the memory of my father, who was the first encourager and supporter to me in continuing my education. iii
<abstract><p>In this paper, we investigate a multi-order $ \varrho $-Hilfer fractional pantograph implicit differential equation on unbounded domains $ (a, \infty), a\geq 0 $. The existence and uniqueness of solution are established for a such problem by utilizing the Banach fixed point theorem in an applicable Banach space. In addition, stability of the types Ulam-Hyers ($ \mathcal UH $), Ulam-Hyers-Rassias ($ \mathcal UHR $) and semi-Ulam-Hyers-Rassias (s-$ \mathcal UHR $) are discussed by using nonlinear analysis topics. Finally, a concrete example includes some particular cases is enhanced to illustrate rightful of our results.</p></abstract>
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