New fixed point theorems for $${\alpha}$$ - $${H\Theta}$$ -contractions in ordered metric spaces.

Recently, Jleli and Samet [J. Inequal. Appl. (2014), 2014:38] introduced and studied a new contraction to prove a generalization of the Banach contraction principle. In this paper, we introduce the concept of $${\alpha}$$ - $${H\Theta}$$ -contraction with respect to a general family of functions H and we establish Jleli-Samet-type fixed point results in metric and ordered metric spaces. As an application of our results we deduce Suzuki-type fixed point results for $${H\Theta}$$ -contractions. We also derive certain fixed and periodic point results for orbitally continuous generalized $${\Theta}$$ -contractions. Moreover, we present an illustrative example to highlight the obtained improvements. [ABSTRACT FROM AUTHOR]