Generalized diamond-a dynamic opial inequalities
نویسندگان
چکیده
* Correspondence: billur@cankaya. edu.tr Department of Mathematics and Computer Science, Çankaya University, Ankara, Turkey Full list of author information is available at the end of the article Abstract We establish some new dynamic Opial-type diamond alpha inequalities in time scales. Our results in special cases yield some of the recent results on Opial’s inequality and also provide new estimates on inequalities of this type. Also, we introduce an example to illustrate our result. Mathematics Subject Classification 2000: 39A12; 26D15; 49K05
منابع مشابه
Dynamic Opial diamond-α integral inequalities involving the power of a function
In this paper, we present some new dynamic Opial-type diamond alpha inequalities on time scales. The obtained results are related to the function [Formula: see text].
متن کاملDynamic Systems and Applications 24 (2015) 229-242 IMPROVEMENTS OF DYNAMIC OPIAL-TYPE INEQUALITIES AND APPLICATIONS
ABSTRACT. In this paper, we present some new improvements of dynamic Opial-type inequalities of first and higher order on time scales. We employ the new inequalities to prove several results related to the spacing between consecutive zeros of a solution and/or a zero of its derivative of a second-order dynamic equation with a damping term. The main results are proved by making use of a recently...
متن کاملOpial–type Inequalities for Fractional Integral Operator Involving Mittag––leffler Function
In this paper we give generalization of Opial-type inequalities by using generalized fractional integral operator involving generalized Mittag–Leffler function. We deduce some results which already have been proved. Also we consider n -exponential convexity of some non-negative differences of inequalities involving Mittag-Leffler function and deduce their exponential convexity and log-convexity.
متن کاملSome New Opial Dynamic Inequalities with Weighted Functions on Time Scales
In this paper we prove some new dynamic inequalities with two weight functions and some new dynamic inequalities with two unknown functions of Opial type on time scales. The main results will be proved by employing Hölder’s inequality, the chain rule and some basic algebraic inequalities. Mathematics subject classification (2010): 26A15, 26D10, 26D15, 39A13, 34A40.
متن کاملOPIAL TYPE Lp-INEQUALITIES FOR FRACTIONAL DERIVATIVES
This paper presents a class of Lp-type Opial inequalities for generalized fractional derivatives for integrable functions based on the results obtained earlier by the first author for continuous functions (1998). The novelty of our approach is the use of the index law for fractional derivatives in lieu of Taylor’s formula, which enables us to relax restrictions on the orders of fractional deriv...
متن کامل