According to the second article, 'Is Jesus a Buddhist':
Will Durant points out that after Alexander's Eastern conquests, the great Indian ruler Ashoka 'sent Buddhist missionaries to all parts of India and Ceylon, even to Syria, Egypt and Greece.'
In fact, Buddhism was prominent in the eastern Hellenic world and became the official religion in several successor states to Alexander's empire: the Greco-Bactrian kingdom (250 - 125 BC) and the Indo-Greek kingdom of Yavanarajva (180 - 10 BC) of which King Menander I was known as a great patron of Buddhism and of whom an important Buddhist text, the Milanda Panha is named after. Wikipedia also notes that the Greek-Buddhist missionary, Dharmaraksitra, was charged by Ashoka to proselytise the faith in north western India where Greek communities were concentrated. The evidence for this coming from the historical Pali texts, the Dipavamsa and the Mahavamsa.
Moreover, there is concrete evidence that Buddhism reached Egypt: Buddhist gravestones decorated with the dharma wheel have been found from the Ptolomeic era, and so a couple of centuries before Christ.
Wikipedia also notes that:
The teachings of the Buddha ... display certain similarities to certain Christian moral precepts more than five centuries later - the sanctity of life, compassion for others, rejection of violence, confession, an emphasis on charity and the practise of virtue.
Given all this, it is quite possible that Christ had been influenced by Buddhist teachings, amongst others. However, given that we know next to nothing about the historical Christ this can only remain speculation.
It's worth pointing out, again in Wikipedia, that several prominent early Christian fathers, Clement of Alexandria and St Jerome were certainly aware of the Buddha and had mentioned him. For example, Clement wrote in book XV in his Stromata:
Some, too, of the Indians obey the precepts of Buddha; who on account of his extraordinary sanctity, they have raised to divine honours.
Interestingly, the parallels between the Jesus and that of the Buddha had been noted long ago in a Tibetan text discovered in Kashmir by Dr Fida Hassnain and which had been translated from an ancient Chinese source called The Glass Mirror. This states:
Yesu, the teacher and founder of religion, who was born miraculously, proclaimed himself Saviour of the World. He commanded his disciples to observe the ten vows [the ten commandments] amongst which is a prohibition against manslaughter and attainment of eternal joy through good deeds. He preached that evil actions plunge oneself into hell, where there is eternal torment and misery. A sin committed in consciousness cannot be confined or pardoned. This is one of the virtuous results emerging out of the teachings of the Buddha.
Unfortunately I haven't been able to find dates for the text. Nevertheless, it remains of interest in showing that these parallels had already been noted by Buddhists before westerners in the modern era rediscovered Buddhism.
Karl Jaspers, a historian of religion, noting the striking parallels amongst a range of theologies and philosophies around this time simply says that mankind was ripe for spiritual development and this came in many different ways. He called this the axial age, an age where the spiritual development of humanity pivoted into a new trajectory. This is of apiece in the Islamic tradition which affirms that many different messengers (rasul) for the diverse communities of man.
There is a messenger for every community (Qu'ran 10:47)
Unfortunately the software of my current phone - an iPhone - isn't up to date with SE (or perhaps it's the othe way around) and so I can't respond to commenters in the comments. Hence O'm replying here. I appreciate your patience.
The Middle East had a whole range of different societies living there, as it does today. The Old Testament itself shows influences from as far back as Egypt - not surprisingly. Whilst Judaism was a direct influence on Christ this is no reason to think that other influences may not be possible. In particular, the Hellenic and through that, Buddhism. My feeling is that this is an under-developed area of research and reflects the Western bias of Western Christianity. For example, the above document, The Glass Mirror would have been undoubtably dated otherwise by now and its authenticity gauged.
I've also seen an article discussing significant parallels between what was said by Christ in the New Testament and the saying of the Buddha. Whilst the parallels were striking, I'm not enough of a Buddhist scholar to be able to judge the authenticity of these sayings. It didn't help that the text wasn't referenced. But it was convincing enough to suggest that this is a avenue worth exploring. As Buddhism becomes more popular and understood in the West my feeling is that there is going to be a lot more research on possible influences in both directions, to the eventual benefit of both and which can only benefit humanity.