Kadakal, Mahir; İmdat, Işcan; Kadakal, Huriye

In this paper, by using an identity we obtain some new Hermite-Hadamard type inequalities for functions whose first derivative in absolute value is exponential type P-function by using Hölder and power-mean integral inequalities. Then, the authors compare the results obtained with both Hölder, Hölder-İşcan integral inequalities and prove that the Hölder-İşcan integral inequality gives a better approximation than the Hölder integral inequality. Also, some applications to special means of real numbers are also given.

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Avci, M.; Ayazoglu, R.

The object of this paper is to study a nonlocal problem involving the p(x)-Laplacian where nonlinearities f do not necessarily satisfy the classical conditions, such as Ambrosetti-Rabinowitz condition, but are limited by functions that do satisfy some specific conditions. By using the direct variational approach and the theory of the variable exponent Sobolev spaces, the existence and uniqueness of solutions is obtained.

AtıfScopus1

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