$m$-convex function
در نشریات گروه ریاضی-
The objective of this paper is to reveal that an analogue of Jensen's inequality holds for positive unital linear maps and matrix $s$-convex functions. We prove that the restriction to the matrix $s$-convex functions is not necessary in the case of $2 \times 2$ matrices in some sense.
Keywords: Convex Function, $S$-Convex Function, Matrix $S$-Convex Function, $P$-Class Function, Jensen's Inequality -
International Journal Of Nonlinear Analysis And Applications, Volume:16 Issue: 5, May 2025, PP 153 -164In this paper, a new class of nonconvex optimization problem is considered, namely $(h,\varphi)$-$(b,F,\rho)$-convexity is defined for $(h,\varphi)$-differentiable mathematical programming problem. The sufficiency of the so-called Karush-Kuhn-Tucker optimality conditions are established for the considered $(h,\varphi)$-differentiable mathematical programming problem under (generalized) $(h,\varphi)$-$(b,F,\rho)$-convexity hypotheses. Further, the so-called Mond-Weir $(h,\varphi)$-dual problem is defined for the considered $(h,\varphi)$-differentiable mathematical programming problem and several duality theorems in the sense of Mond-Weir are derived under appropriate (generalized) $(h,\varphi)$-$(b,F,\rho)$-convex assumptions.Keywords: $(H, Varphi)$-Differentiable Mathematical Programming, $(H, Varphi)-(B, F, Rho)$-Convex Function, Generalized Algebraic Operations, Optimality Conditions, Duality
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International Journal Of Nonlinear Analysis And Applications, Volume:14 Issue: 4, Apr 2023, PP 47 -54
In the present paper, we introduce two new subclasses of the function class P of bi-univalent functions defined in the open unit disc U. Furthermore, we find estimates on the coefficients |a2| and |a3| for functions in these new subclasses.
Keywords: Bi-univalent function, Analytic function, Coefficient bounds, starlike, convex function -
In this paper, we generalize the Jensen's inequality for $m$-convex functions and we present a correction of Jensen's inequality which is a better than the generalization of this inequality for $m$-convex functions. Finally we have found new lower and upper bounds for Jensen's discrete inequality.
Keywords: Jensen's inequality, $m$-convex function, convex function, Inequality -
International Journal Of Nonlinear Analysis And Applications, Volume:13 Issue: 1, Winter-Spring 2022, PP 2885 -2895
In this paper, (h1,h2)-convex and s-convex functions are merged to form (h1,h2,s)-convex function. Inequalities of the Hermite-Hadamard (H-H) and Fejer's types will then be extended by using the (h1,h2,s)-convex function and its derivatives. Some special cases for these extended H-H and Fejer's inequalities are also explored in order to get the previously specified results. The relationship between newly constructed Hermite-Hadamard (H−H) and Fejer's types of inequalities with the average (mean) values are also discussed.
Keywords: Inequality, Hermite-Hadamard (H-H), Fejer, Convex function -
The aim of this study is to establish some new Caputo fractional integral inequalities. By applying definition of (h − m)-convexity and some straightforward inequalities an upper bound of the sum of left and right sided Caputo fractional derivatives has been established. Furthermore, a modulus inequality and a Hadamard type inequality have been analyzed. These results provide various fractional inequalities for all particular functions deducible from (h − m)-convexity, see Remark 1.3.
Keywords: Convex function, (h − m)-convex function, Caputo fractional derivatives -
Fractional integral operators play an important role in generalizations and extensions of various subjects of sciences and engineering. This research is the study of bounds of Riemann-Liouville fractional integrals via (h − m)-convex functions. The author succeeded to find upper bounds of the sum of left and right fractional integrals for (h − m)-convex function as well as for functions which are deducible from aforementioned function (as comprise in Remark 1.2). By using (h − m) convexity of |f ′ | a modulus inequality is established for bounds of Riemann-Liouville fractional integrals. Moreover, a Hadamard type inequality is obtained by imposing an additional condition. Several special cases of the results of this research are identified.Keywords: Convex function, (h − m)-convex function, Riemann-Liouville fractional integral operators, Bounds
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در این مقاله، ما یک تابع (⊗,⊕)- محدب کلی را بر اساس نیم حلقه های، (⊗ ,⊕, [b, a([با شبه -جمع ⊕ و شبه-ضرب ⊗ معرفی میکنیم. تعمیم نامساوی Jensen متناهی و همچنین شبه – انتگرال نسبت به توابع (⊗,⊕) – محدب بدست آمده است. این نیز نامساویهای Jensen برای انتگرال لبگ و نتایج پاپ و استربوجا را تعمیم میدهد [12 . [در ضمن، نامساویهای Jensen را نیز برای شبه-انتگرالها روی نیم حلقه های (⊗ ,Sup], b, a ([نسبت به توابع غیرنزولی اثبات و نتایج متناظر برای انتگرال های فازی تعمیم یافته را ارایه میدهیم.
In this paper, we introduce a general$(oplus,otimes)$-convex function based on semirings $([a,b],oplus, otimes)$ with pseudo-addition $oplus$ andpseudo-multiplication $otimes.$ The generalization of the finiteJensen's inequality, as well as pseudo-integral with respect to$(oplus,otimes)$-convex functions, is obtained. This also generalizes Jensen's inequalities for Lebesgue integral and the results of Pap and v{S}trboja cite{12}. Meanwhile, we also prove Jensen's inequalities for pseudo-integrals on semirings $([a,b], sup, otimes)$with respect to nondecreasing functions and present correspondingresults for generalized fuzzy integrals.
Keywords: Jensen's inequality, Semiring, pseudo-integral, pseudo-operation, $(oplus, otimes)$-convex function -
International Journal Of Nonlinear Analysis And Applications, Volume:12 Issue: 1, Winter-Spring 2021, PP 2339 -2352
In this paper, we give an upper bound for the fourth Hankel determinant H4(1) for a new class S#C associated with the sine function.
Keywords: analytic functions, univalent functions, fourth-order Hankel determinant, subordination, convex function, sine function -
In the present paper, we introduce and investigate three interesting superclasses SD, SD* and KD of analytic, normalized and univalent functions in the open unit disk D. For functions belonging to these classes SD, SD* and KD, we derive several properties including (for example) the coefficient bounds and growth theorems. The various results presented here would generalize many well known results. We also get a new univalent criterion and some interesting properties for univalent function,starlike function,convex function and close-to-convex function. Many superclasses which are already studied by various researchers are obtained as special cases of our two new superclasses.
Keywords: Univalent functions, starlike functions, Convex functions, Close-to-convex function -
International Journal of Mathematical Modelling & Computations, Volume:10 Issue: 1, Winter 2020, PP 57 -75This article deals with the different classes of convexity and generalizations. Firstly, we reveal the new generalization of the definition of convexity that can reduce many order of convexity. We have showed features of algebra for this new convex function. Then after we have constituted Hermite-Hadamard type inequalities for this class of functions. Finally the identity has been revealed for its by us and by using this identity, then theorems and corollaries have been obtained.Keywords: $M, {varphi }A$-convex function, Hermite-Hadamard type inequality, $GA$-convex function, convex function, harmonically convex function
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Using the notion of eta-convex functions as generalization of convex functions, we estimate the difference between the middle and right terms in Hermite-Hadamard-Fejer inequality for differentiable mappings. Also as an application we give an error estimate for midpoint formula.Keywords: eta, convex function, Hermite, Hadamard, Fejer inequality
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In the present paper, we prove subordination, superordination and sandwich-type properties of a certain integral operators for univalent functions on open unit disc, moreover the special behavior of this class is investigated.Keywords: Analytic function, Starlike, convex function, Univalent function, Dierential subordination, superordination, Bounded rotation
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