• Journal of applied mathematics & informatics
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• 제32권3_4호
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• pp.491-502
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• 2014

In this paper, by using the notion of ${\rho}$-(p,r)-invexity assumptions on the functions involved, optimality conditions and duality results (Mond-Weir, Wolfe and mixed type) are established on differentiable manifolds. Counterexample is constructed to justify that our investigations are more general than the existing work available in the literature.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1381-1395
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• 2009

Mixed type second order dual to the non-differentiable problem containing support functions is formulated and duality theorems are proved under generalized second order convexity conditions. It is pointed out that the mixed type duality results already reported in the literature are the special cases of our results.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권1호
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• pp.85-98
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• 2009

Strong convergence theorems on viscosity approximation methods for finite nonexpansive mappings are established in Banach spaces. The main theorem generalize the corresponding result of Kim and Xu [10] to the viscosity approximation method for finite nonexpansive mappings in a reflexive Banach space having a uniformly Gateaux differentiable norm. Our results also improve the corresponding results of [7, 8, 19, 20].

• East Asian mathematical journal
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• 제24권3호
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• pp.295-304
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• 2008

We approximate a locally unique solution of a nonlinear operator equation containing a non-differentiable operator in a Banach space setting using Newton's method. Sufficient conditions for the semilocal convergence of Newton's method in this case have been given by several authors using mainly increasing sequences [1]-[6]. Here, we use center as well as Lipschitz conditions and decreasing majorizing sequences to obtain new sufficient convergence conditions weaker than before in many interesting cases. Numerical examples where our results apply to solve equations but earlier ones cannot [2], [5], [6] are also provided in this study.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권4호
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• pp.345-351
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• 2011

Taylor's formula is a powerful tool in analysis. In this study, we assume that an operator is m-times Fr$\acute{e}$chet-differentiable and satisfies a Lipschitz condition. We then obtain some Taylor formulas using only the Lipschitz constants. Applications are also provided.

• 호남수학학술지
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• 제44권2호
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• pp.244-258
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• 2022

In this work, by using an integral identity together with both the Hölder and the power-mean integral inequalities we establish several new inequalities for n-times differentiable arithmetic-harmonically-convex function. Then, using this inequalities, we obtain some new inequalities connected with means. In special cases, the results obtained coincide with the well-known results in the literature.

• 호남수학학술지
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• 제45권1호
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• pp.160-183
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• 2023

In the present paper, we prove that our main inequality reduces to some trapezoid and Newton type inequalities for differentiable s-convex functions. These inequalities are established by using the well-known Riemann-Liouville fractional integrals. With the help of special cases of our main results, we also present some new and previously obtained trapezoid and Newton type inequalities.

• 호남수학학술지
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• 제45권2호
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• pp.285-299
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• 2023

In the present paper, we establish some perturbed Newton-type inequalities in the case of twice differentiable convex functions. These inequalities are established by using the well-known Riemann-Liouville fractional integrals. With the aid of special cases of our main results, we also give some previously obtained Newton-type inequalities.

• 호남수학학술지
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• 제7권1호
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• pp.35-55
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• 1985

• Kyungpook Mathematical Journal
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• 제14권1호
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• pp.23-36
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• 1974