جستجوی مقالات مرتبط با کلیدواژه « Hermite-Hadamard inequality » در نشریات گروه « ریاضی »

New variants of the Hermite - Hadamard inequality within the framework of generalized fractional integrals for $(h,m,s)$-convex modified second type functions have been obtained in this article. To achieve these results, we used the Holder inequality and another form of it - power means. Some of the known results described in the literature can be considered as particular cases of the results obtained in our study.

In this paper, we study the concept of exponential convex functions with respect to $s$ and prove Hermite-Hadamard type inequalities for the newly introduced this class of functions. In addition, we get some refinements of    the Hermite-Hadamard (H-H) inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is exponential convex with respect to $s$. Our results coincide with the results obtained previously in special cases.

In this paper, for generalised preinvex functions, new estimates of the Fej\'{e}r-Hermite-Hadamard inequality on fractional sets $\mathbb{R}^{\rho }$ are given in this study. We demonstrated a fractional  integral inequalities based on Fej\'{e}r-Hermite-Hadamard theory. We establish two new local fractional integral identities for differentiable functions. We construct several novel Fej\'{e}r-Hermite-Hadamard-type inequalities for generalized convex function in local fractional calculuscontexts using these integral identities. We provide a few illustrations to highlight the uses of the obtained findings. Furthermore, we have also given a few examples of new inequalities in use.

In this paper we introduce a new sequence of mappings in connection to Hermite-Hadamard type inequality. Some bounds and refinements of Hermite-Hadamard inequality for convex functions via this  sequence  are given

‎We obtain some new Jensen-Mercer type inequalities for log-convex functions‎. ‎Indeed‎, ‎we establish refinement and reverse for the Jensen-Mercer inequality for log-convex functions‎. ‎Several new Hermite-Hadamard and Fej\'er types of inequalities are also presented‎.‎

In this paper we introduce two new mapping in connection to Hermite-Hadamard type inequality. Some results concerning these mappings associated to the celebrated Hermite-Hadamard integral inequality for preinvex functions are given.

This paper is concerned to establish new variants of the well-known Hermite-Hadamard (HH) inequality for 3-times differentiable functions. Under the utility of these identities, we establish some new inequalities for the class of functions whose absolute value of the third derivative are MT-convex. The results presented here would provide generalizations of those given in earlier works. Finally, we present applications of our findings for means of real numbers and applications for particular functions are pointed out.

By use of definition of a generalized fractional integral operators, proposed by Raina and Agarwal et.al, we establish a fractional  Hermite-Hadamard type inequalities for p−convex functions and an identity with a parameter. We derive several parameterized  integral inequalities associated with this identity, and provide two examples to illustrate the obtained results.

In this paper, we establish some inequalities for generalized fractional integrals by utilizing the assumption that the second derivative of $phi (x)=varpi left( frac{kappa _{1}kappa _{2}}{mathcal{varkappa }}right)  $ is bounded. We also prove again a Hermite-Hadamard type inequality obtained in [34] under the condition $phi ^{prime }left( kappa_{1}+kappa _{2}-mathcal{varkappa }right) geq phi ^{prime }(mathcal{varkappa })$ instead of harmonically convexity of $varpi $. Moreover, some new inequalities for $k$-fractional integrals are given as special cases of main results.

Let $f$ be a convex function on $I$ and $a,$ $bin I$ with $a<b.$ If $p:% left[ a,bright] rightarrow lbrack 0,infty )$ is Lebesgue integrable and symmetric, namely $pleft( b+a-tright) =pleft( tright) $ for all $tin % left[ a,bright] ,$ then we show in this paper that begin{align*} 0& leq frac{1}{2}int_{a}^{b}leftvert t-frac{a+b}{2}rightvert pleft( tright) dtleft[ f_{+}^{prime }left( frac{a+b}{2}right) -f_{-}^{prime }left( frac{a+b}{2}right) right]  \ & leq int_{a}^{b}pleft( tright) fleft( tright) dt-left( int_{a}^{b}pleft( tright) dtright) fleft( frac{a+b}{2}right)  \ & leq frac{1}{2}int_{a}^{b}leftvert t-frac{a+b}{2}rightvert pleft( tright) dtleft[ f_{-}^{prime }left( bright) -f_{+}^{prime }left( aright) right] end{align*} and begin{align*} 0& leq frac{1}{2}int_{a}^{b}left[ frac{1}{2}left( b-aright) -leftvert t-frac{a+b}{2}rightvert right] pleft( tright) dtleft[ f_{+}^{prime }left( frac{a+b}{2}right) -f_{-}^{prime }left( frac{a+b}{% 2}right) right]  \ & leq left( int_{a}^{b}pleft( tright) dtright) frac{fleft( aright) +fleft( bright) }{2}-int_{a}^{b}pleft( tright) fleft( tright) dt \ & leq frac{1}{2}int_{a}^{b}left[ frac{1}{2}left( b-aright) -leftvert t-frac{a+b}{2}rightvert right] pleft( tright) dtleft[ f_{-}^{prime }left( bright) -f_{+}^{prime }left( aright) right] . end{align*}.

‎Let $left( H;leftlangle cdot‎ ,‎cdot rightrangle right)$ be a complex‎ ‎Hilbert space‎. ‎Denote by $mathcal{B}left( Hright)$ the Banach $C^{ast }$-‎algebra of bounded linear operators on $H$‎. ‎For $Ain mathcal{B}left(‎Hright)$ we define the modulus of $A$ by $leftvert Arightvert‎ :‎=left(‎A^{ast }Aright) ^{1/2}$ and $func{Re}A:=frac{1}{2}left( A^{ast‎‎}+Aright)‎.‎$ In this paper we show among other that‎, ‎if $A,$ $Bin mathcal{‎‎B}left( Hright)$ with $0leq mleq leftvert left( 1-tright)‎‎A+tBrightvert ^{2}leq M$ for all $tin left[ 0,1right]‎,‎$ then begin{align*}‎ ‎0& leq int_{0}^{1}fleft( leftvert left( 1-tright) A+tBrightvert‎‎^{2}right) dt-fleft( frac{leftvert Arightvert ^{2}+func{Re}left(‎‎B^{ast }Aright)‎ +‎leftvert Brightvert ^{2}}{3}right) \‎ ‎& leq 2left[ frac{fleft( mright)‎ +‎fleft( Mright) }{2}-fleft( frac{‎m+M}{2}right) right] 1_{H}‎ ‎end{align*} ‎for operator convex functions $f:[0,infty )rightarrow mathbb{R}$‎. ‎Applications for power and logarithmic functions are also provided‎.

In this paper, we first establish two new identities for differentiable function involving generalized fractional integrals. Then, by utilizing these equalities, we obtain some midpoint type inequalities involving generalized fractional integrals for mappings whose derivatives in absolute values are convex. We also give several results as special cases of our main results.

Here our aim is to prove the Hermite-Hadamard and Fejér inequalities for p-convex functions via Caputo fractional derivatives. We also establish some useful identities in order to find further Hadamard’s and Fejér type inequalities which are generalizations of the results given in the literature cited here.

In this paper we prove several sharp inequalities that are new versions and  extensions of Jensen and $H-H$ inequalities. Then we apply them on means.

In this article, we introduce the notion of $(h,k)$-convex functions and their operator form. Moreover, we derive Hermite–Hadamard-type, and Fejer-type inequalities for this class.

In this paper, we establish some Trapezoid and Midpoint type inequalities for generalized fractional integrals by utilizing the functions whose second derivatives are bounded . We also give some new inequalities for $k$-Riemann-Liouville fractional integrals as special cases of our main results. We also obtain some Hermite-Hadamard type inequalities by using the condition $f^{prime }(a+b-x)geq f^{prime }(x)$ for all $xin left[ a,frac{a+b}{2}right] $ instead of convexity.

In this paper, we first prove a lemma for twice differentiable functions . Then we establish some inequalities for mapping whose second derivatives in absolute value are convex via Riemann-Liouville fractional integrals. These results generalize the midpoint and trapezoid inequalities involving Riemann-Liouville fractional integrals given in earlier studies.

In this study, we first introduce the co-ordinated hyperbolic ρ-convex functions. Then we establish some Hermite-Hadamard type inequalities for co-ordinated hyperbolic ρ-convex functions. The inequalities obtained in this study provide generalizations of some results given in earlier works.

In this paper, authors discover two interesting identities regarding Gauss--Jacobi and trapezium type integral inequalities. By using the first lemma as an auxiliary result, some new bounds with respect to Gauss--Jacobi type integral inequalities for a new class of functions called strongly $(h_{1},h_{2})$--preinvex of order $sigma>0$ with modulus $mu>0$ via general fractional integrals are established. Also, using the second lemma, some new estimates with respect to trapezium type integral inequalities for strongly $(h_{1},h_{2})$--preinvex functions of order $sigma>0$ with modulus $mu>0$ via general fractional integrals are obtained. It is pointed out that some new special cases can be deduced from main results. Some applications to special means for different real numbers and new approximation error estimates for the trapezoidal are provided as well. These results give us the generalizations of some previous known results. The ideas and techniques of this paper may stimulate further research in the fascinating field of inequalities.