@article{(Open Science Index):https://publications.waset.org/pdf/10006191, title = {Algorithms for Computing of Optimization Problems with a Common Minimum-Norm Fixed Point with Applications}, author = {Apirak Sombat and Teerapol Saleewong and Poom Kumam and Parin Chaipunya and Wiyada Kumam and Anantachai Padcharoen and Yeol Je Cho and Thana Sutthibutpong}, country = {}, institution = {}, abstract = {This research is aimed to study a two-step iteration process defined over a finite family of σ-asymptotically quasi-nonexpansive nonself-mappings. The strong convergence is guaranteed under the framework of Banach spaces with some additional structural properties including strict and uniform convexity, reflexivity, and smoothness assumptions. With similar projection technique for nonself-mapping in Hilbert spaces, we hereby use the generalized projection to construct a point within the corresponding domain. Moreover, we have to introduce the use of duality mapping and its inverse to overcome the unavailability of duality representation that is exploit by Hilbert space theorists. We then apply our results for σ-asymptotically quasi-nonexpansive nonself-mappings to solve for ideal efficiency of vector optimization problems composed of finitely many objective functions. We also showed that the obtained solution from our process is the closest to the origin. Moreover, we also give an illustrative numerical example to support our results.}, journal = {International Journal of Mathematical and Computational Sciences}, volume = {10}, number = {12}, year = {2016}, pages = {688 - 696}, ee = {https://publications.waset.org/pdf/10006191}, url = {https://publications.waset.org/vol/120}, bibsource = {https://publications.waset.org/}, issn = {eISSN: 1307-6892}, publisher = {World Academy of Science, Engineering and Technology}, index = {Open Science Index 120, 2016}, }