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This paper proves a new q-Hermite-Hadamard inequality for convex functions using quantum integrals. We also prove some new midpoint-type inequalities for q-differentiable convex functions. Moreover, we present some examples to illustrate our established results, supplemented with graphs. [ABSTRACT FROM AUTHOR]

In this paper, some sufficient conditions for the oscillation of all solutions of second order dynamic equations with a negative sub-linear neutral term are established. The obtained results provide a unified platform that adequately covers both discrete and continuous equations. Furthermore, it covers a wide range of equations by utilizing different time scales. Illustrative examples are provided. [ABSTRACT FROM AUTHOR]

In this research paper, we investigate some new identifies for Sarıkaya fractional integrals which introduced by Sarıkaya and Ertugral in [20]. The fractional integral operators also have been applied to Hermite-Hadamard type integral inequalities to provide their generalized properties. Furthermore, as special cases of our main results, we present several known inequalities such as Simpson, Bullen, trapezoid for convex functions. [ABSTRACT FROM AUTHOR]

The aim of this paper is to improve some fixed point results given by I.A. Rus in (On a fixed point theorem of Maia, Studia Univ. Babes¸-Bolyai Math., 22(1977), 40-42), (Basic problem for Maia's theorem, Sem. on Fixed Point Theory, Preprint 3(1981), Babes¸-Bolyai Univ. Cluj- Napoca, 112-115) and (Data dependence of the fixed points in a set with two metrics, Fixed Point Theory, 8(2007), no. 1, 115-123), by applying, instead of contraction principle, some variants of Maia's fixed point theorem. 2010 Mathematics Subject Classification: 47H10, 47H09, 34K05, 34K12, 45D05, 45G10, [ABSTRACT FROM AUTHOR]

In this paper, we show that the contractive definition considered by Proinov [Fixed point theorems in metric spaces, Nonlinear Analysis 64 (2006) 546 - 557] is strong enough to generate a fixed point but does not force the mapping to be continuous at the fixed point. Thus we provide several answers to the open question posed by B.E. Rhoades in Contractive definitions and continuity, Contemporary Mathematics 72(1988), 233-245. [ABSTRACT FROM AUTHOR]

In this paper, we extend relation-theoretic contraction principle due to Alam and Im- dad to a nonlinear contraction using a relatively weaker class of continuous control functions employing a locally finitely T -transitive binary relation, which improves the corresponding fixed point theorems especially due to: Alam and Imdad (J. Fixed Point Theory Appl. 17 (2015) 693-702), Agarwal et al: (Applicable Analysis, 87 (1) (2008) 109-116), Berzig and Karapinar (Fixed Point Theory Appl. 2013:205 (2013) 18 pp), Berzig et al: (Abstr. Appl. Anal. 2014:259768 (2014) 12 pp) and Turinici (The Sci. World J. 2014:169358 (2014) 10 pp). [ABSTRACT FROM AUTHOR]