In the article, we establish some new general fractional integral inequalities for exponentially m-convexfunctions involving an extended Mittag-Leffler function, provide several kinds of fractional integral operator ...
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In the article, we establish some new general fractional integral inequalities for exponentially m-convexfunctions involving an extended Mittag-Leffler function, provide several kinds of fractional integral operator inequalities and give certain special cases for our obtained results.
The visual beauty reflects the practicability and superiority of design dependent on the fractal theory. Based on the applicability in practice, it shows that it is the completely feasible, self-comparability and mult...
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The visual beauty reflects the practicability and superiority of design dependent on the fractal theory. Based on the applicability in practice, it shows that it is the completely feasible, self-comparability and multifaceted nature of fractal sets that made it an appealing field of research. There is a strong correlation between fractal sets and convexity due to its intriguing nature in the mathematical sciences. This paper investigates the notions of generalized exponentially harmonically (GEH) convex and GEH s-convexfunctions on a real linear fractal sets R-alpha (0 < alpha =<= 1). Based on these novel ideas, we derive the generalized Hermite-Hadamard inequality, generalized Fejer-Hermite-Hadamard type inequality and Pachpatte type inequalities for GEH s-convexfunctions. Taking into account the local fractal identity;we establish a certain generalized Hermite-Hadamard type inequalities for local differentiable GEH s-convexfunctions. Meanwhile, another auxiliary result is employed to obtain the generalized Ostrowski type inequalities for the proposed techniques. Several special cases of the proposed concept are presented in the light of generalized exponentially harmonically convex, generalized harmonically convex and generalized harmonically s-convex. Meanwhile, an illustrative example and some novel applications in generalized special means are obtained to ensure the correctness of the present results. This novel strategy captures several existing results in the corresponding literature. Finally, we suppose that the consequences of this paper can stimulate those who are interested in fractal analysis.
In this paper we obtain two means for divide differences using two majorization type results where one is related with Schur convexity. We examine their monotonicity property using exponentially convex functions.
In this paper we obtain two means for divide differences using two majorization type results where one is related with Schur convexity. We examine their monotonicity property using exponentially convex functions.
In this paper, we investigate n-exponential convexity and log-convexity using the positive functional defined as the difference of the left-hand side and right-hand side of the inequality from (Pecaric and Janic in Fa...
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In this paper, we investigate n-exponential convexity and log-convexity using the positive functional defined as the difference of the left-hand side and right-hand side of the inequality from (Pecaric and Janic in Facta Univ., Ser. Math. Inform. 3:39-42, 1988). We also give mean value theorems of Lagrange and Cauchy types. Finally, we construct means with Stolarsky property.
In this paper we obtain means which involve divided differences for n-convexfunctions. We examine their monotonicity property using exponentially convex functions.
In this paper we obtain means which involve divided differences for n-convexfunctions. We examine their monotonicity property using exponentially convex functions.
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